For this minimization problem, we use the same deep learning guided memetic framework presented in the last subsections. The only parts of the general framework that require specific adaptations for the \(k\) -COL concern the initialization and the parallel local search. For the \(k\) -COL, we use a pure random initialization procedure. At the beginning, for each individual of the population, each node \(v \in V\)  receives a random color in \(\lbrace 1, \dots , k \rbrace \) . For the local search, we run in parallel the popular TabuCOL algorithm [1]} (i.e., its efficient implementation presented in [2]}) on the GPU to raise the quality of the current population during \(128 \times |V|\)  iterations, where \(|V|\)  is the order of the graph. TabuCOL is launched with its default parameters setting like in [3]}.
